RU2492456C1 - Method of determining characteristics of pore volume and thermal conductivity of matrix of porous materials - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: for determining the characteristics of pore volume and thermal conductivity of matrix of samples of porous materials, the sample of porous material is alternately saturated with at least two fluids with different known thermal conductivity. As at least one saturating fluid a mixture of fluids from at least two fluids with different known thermal conductivity is used. After each saturation of the sample the thermal conductivity of the saturated sample of the porous material is measured, and the characteristics of pore volume and thermal conductivity of the matrix of the sample of porous material is determined taking into account the results of thermal conductivity measurements.

EFFECT: increased accuracy and stability of determining the characteristics of the pore volume and the thermal conductivity of the test samples.

14 cl, 2 dwg

Description

Technical field

The invention relates to the field of studying the physical properties of porous inhomogeneous materials, namely, to determining the characteristics of the pore space and thermal conductivity of the matrix (space filled only with solid substance) of these materials.

Porous heterogeneous materials may include, for example, industrial materials, loose and consolidated rock samples, and minerals.

State of the art

A known method for determining the characteristics of the pore space and thermal conductivity of a matrix for a porous material sample by measuring the thermal conductivity of a sample successively saturated with three fluids with different thermal conductivity (Popov et al. Interrelations between thermal conductivity and other physical properties of rocks: experimental data. Pure and Appl. Geophys. , 160, 2003, pp1137-1161). The method is based on determining the porosity of a sample of a porous material, thermal conductivity of the matrix, and the shape of pores and cracks, which are modeled by rotation ellipsoids and are characterized by one aspect ratio. The porosity of a sample of a porous material, the thermal conductivity of the matrix, and the aspect ratio of ellipsoids modeling pores and cracks are determined by solving a system of three nonlinear equations with three unknowns using measurements of thermal conductivity on a sample of a porous material sequentially saturated with three fluids with known different thermal conductivity. Equations in this system are the equal values of the theoretical and experimental thermal conductivity of samples of pore material, sequentially saturated with three fluids with known different thermal conductivity. The theoretical values of thermal conductivity are determined using the well-known method of self-consistency of the theory of effective media, which allows us to express the value of the thermal conductivity of a porous material depending on the thermal conductivity of the matrix, fluid filling pores and cracks, porosity and aspect ratio of ellipsoids. The disadvantages of this method are as follows: (1) one aspect ratio is used to characterize the shape of both pores and cracks, the aspect ratio of which actually differs by several orders of magnitude, (2) the method requires sequential saturation of the porous material sample with three different fluids, whose thermal conductivity must meet the following three conditions: a) it must be known for each fluid, b) it must have substantially different values, each of which should be selected in advance according to According to certain requirements, in accordance with the thermal conductivity, porosity and pore space characteristics of the studied porous inhomogeneous materials, c) the thermal conductivity of these three fluids should be in a certain range of values, which should be selected in advance depending on the thermal conductivity, porosity and characteristics of the pore space of the studied porous inhomogeneous materials . The fulfillment of the last three conditions is a serious problem due to the lack of such prepared fluids in nature. In addition, the disadvantage of this known method is the lack of accuracy in determining the characteristics of the pore space and thermal conductivity of the matrix due to the fact that they are limited only to measurements of the thermal conductivity of fluid-saturated porous inhomogeneous material and do not use the results of additional measurements of other physical properties, which may include, for example, longitudinal or transverse velocity of elastic waves, electrical conductivity, hydraulic and dielectric constant, density, volume specific heats.

The closest analogue of the claimed method is a method for determining the characteristics of the pore space and thermal conductivity of the matrix (Popov et al. Physical properties of rocks from the upper part of the Yaxcopoil-1 drill hole, Chicxulub crater. Meteoritics & Planetary Science, 39, Nr 6, 2004, pp799-812), which consists in sequentially saturating a sample of a porous material with at least two fluids with known different thermal conductivity and determining the porosity of the sample. After each saturation of the sample of the porous material with a fluid, the thermal conductivity of the sample is measured. From the totality of the results of measurements of the thermal conductivity and porosity of the sample of the porous material, the characteristics of the pore space and the thermal conductivity of the matrix of the sample of the porous material are determined by the known ratio.

The disadvantages of this method are the following: (1) more than two unknown values are determined only by two measurements of thermal conductivity, which leads to the possibility of the existence of a fairly wide range of different solutions for the characteristics of the pore space and thermal conductivity of the matrix; (2) porosity must be known in advance; (3) the method requires sequentially saturating the sample of the porous material with two different fluids, the thermal conductivity of which must meet the following two conditions: a) it must be known for each fluid, b) it must have significantly different values in a range that must be selected in advance in accordance with thermal conductivity, porosity and pore space characteristics of the studied porous inhomogeneous materials. The fulfillment of the last two conditions is a serious problem due to the lack of such prepared fluids in nature. In addition, the disadvantage of this known method is the lack of accuracy in determining the characteristics of the pore space and thermal conductivity of the matrix due to the fact that they are limited only to measurements of the thermal conductivity of fluid-saturated porous inhomogeneous material and do not use the results of additional measurements of other physical properties, which may include, for example, longitudinal or transverse velocity of elastic waves, electrical conductivity, hydraulic and dielectric constant, density, volume specific heats.

Disclosure of invention

The technical result achieved by the implementation of the present invention is to increase the stability of determining the characteristics of the pore space and thermal conductivity of the matrix due to the use of mixtures of two or more fluids with different thermal conductivity as additional saturating substances. This leads to the possibility of saturating the studied porous inhomogeneous materials with fluids with a predetermined thermal conductivity and an increase in the number of experimental values of physical properties (thermal conductivity and other properties, including, for example, elastic wave velocities, electrical conductivity, hydraulic and dielectric constant, density, volumetric heat capacity), which are used to determine unknown parameters - the characteristics of the pore space and thermal conductivity of the matrix. The thermal conductivity of the mixtures thus prepared can be determined (by measurement or calculation) and is known for each mixture. In addition, the thermal conductivity of such mixtures can have significantly different values, each of which can be pre-selected in accordance with certain requirements in accordance with the thermal conductivity, porosity and pore space characteristics of the studied porous inhomogeneous materials. In addition, the condition can be fulfilled, according to which the thermal conductivity of these fluid mixtures is in a certain range of values, which can be selected in advance depending on the thermal conductivity, porosity and characteristics of the pore space of the studied porous inhomogeneous materials. The possibility of increasing the number of saturating substances due to the use of mixtures of two or more fluids with different, including predetermined, thermal conductivity also allows us not to require that the porosity of the porous material be known in advance, but to include it among the determined quantities along with the characteristics of the pore space and thermal conductivity matrices.

The specified technical result is achieved due to the fact that the sample of the porous material is alternately saturated with at least two fluids with different known thermal conductivity, and a mixture of fluids of at least two fluids with different known thermal conductivity is used as at least one saturating fluid. After each saturation of the sample, the thermal conductivity of the saturated sample of the porous material is measured and the characteristics of the pore space and thermal conductivity of the matrix of the sample of the porous material are determined taking into account the results of measurements of thermal conductivity. Pore space characteristics include porosity and geometrical parameters of the pore space. In another embodiment, the porosity of the samples of porous materials can be determined in advance.

The thermal conductivity of the fluid mixture can be determined previously from the known thermal conductivity of each of the mixed fluids and the proportion of volumes or masses of the mixed fluids. According to another embodiment of the invention, the thermal conductivity of the fluid mixture can be determined by measuring the thermal conductivity of the mixture after mixing the fluids.

According to another embodiment of the invention, the thermal conductivity value or the thermal conductivity range of the fluid mixture is predetermined.

Oil and water may be used as fluids.

As at least one of the fluids of the mixture can be used a gas with known thermal conductivity, for example, air. When using at least two fluid mixtures containing a gas with known thermal conductivity, different thermal conductivity of the mixtures is achieved by using the same gas with different humidity.

In accordance with one embodiment of the invention, the necessary values of the thermal conductivity of the fluids, the number of prepared fluid mixtures and the thermal conductivity of the prepared fluid mixtures are preliminarily determined.

In accordance with another embodiment of the invention, after each saturation of the porous material sample, at least one additional physical property of the sample is measured, and the results of determining the additional physical property of the porous material sample are used together with the results of determining the thermal conductivity of the porous material sample to determine the characteristics of the pore space and thermal conductivity of the matrix sample of porous materials.

Additionally, the physical property of the porous material sample can be determined by at least one property from the following group: elastic wave velocities, electrical conductivity, permeability, density, bulk heat capacity.

The thermal conductivity of a saturated sample can be determined by optical scanning.

Brief Description of the Drawings

The invention is illustrated by the drawings shown in figure 1 and figure 2. Figure 1 shows the distribution of the void volume by aspect ratios, constructed from the found Beta distribution parameters (α = 3.0, β = 1.1), in the case when the porosity of the sample was unknown and was the desired parameter along with the Beta distribution parameters and matrix thermal conductivity . Figure 2 shows the distribution of void volume by aspect ratio, constructed from the found Beta distribution parameters (α = 7.1, β = 1.8), in the case when the porosity of the sample was previously known.

The implementation of the invention

In accordance with the proposed method, in addition to saturating a porous material sample with one or more fluids with known thermal conductivity and subsequent measurements of the thermal conductivity of a saturated porous material sample, the sample is saturated with at least one mixture consisting of two or more fluids with different known thermal conductivities. Each time after saturation of a sample of a porous material, its thermal conductivity is measured. The measured values of the thermal conductivity of a sample of a porous material saturated with one or more mixtures of two or more fluids are used to determine the characteristics of the pore space and thermal conductivity of the matrix of the sample of porous material. The characteristics of the pore space include the porosity and geometric parameters of the pore space (for example, the aspect ratio of ellipsoids modeling voids, the parameters of the distribution function of the aspect ratio of pores and cracks, or any other quantities characterizing the shape of pores and cracks, by their volume, orientation, or size).

The porosity, geometrical parameters of the pore space and the thermal conductivity of the matrix for a sample of a porous material are determined so that the discrepancy between the experimental values of the thermal conductivity obtained at each saturation of the sample of the porous material and the theoretical values of the thermal conductivity of the sample of the porous material does not exceed a specified value. The theoretical value of the thermal conductivity of a sample of a porous material depending on the porosity, geometric parameters of the pore space and the thermal conductivity of the matrix is determined using the well-known relation connecting the value of the thermal conductivity of the sample of the porous material with the values of porosity, geometric parameters of the pore space and thermal conductivity of the matrix. For example, for this purpose, the known relations of the methods of the theory of effective media, shown below, can be used.

Let the thermal conductivity measurements be carried out in a certain direction specified by the vector n = (n ₁ , n ₂ , n ₃ ) in the main coordinate system. The main coordinate system is determined by the symmetry elements of the porous material sample and in it the effective thermal conductivity tensor has a diagonal shape. Then, in this direction, the value of thermal conductivity is determined by the well-known formula:

$${\lambda }^{*(n)}={\lambda }_{ij}^{*}{n}_i{n}_j={\lambda }_{\mathrm{eleven}}^{*}{n}_{\mathrm{one}}^2+{\lambda }_{22}^{*}{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="00000028.png,00000029.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^2+{\lambda }_{33}^{*}{\mathrm{<figure-callout\; id="3"\; label="n"\; filenames="00000029.png"\; state="\{\{state\}\}">n</figure-callout>}}_3^2,\left(\mathrm{one}\right)$$

where λ ^* is the effective thermal conductivity tensor in the main coordinate system associated with the porosity ϕ, the geometric parameters of the pore space determined by the tensor g, and the thermal conductivity tensor of the matrix λ ^M as follows (Popov et al., Interrelations between thermal conductivity and other physical properties of rocks : experimental data. Pure Appl. Geophys., 160, 2003, pp. 1137-1161):

$$\begin{array}{l}{\lambda }^{*}=\left[\left(\mathrm{one}-\phi \right)〈{\lambda }^M\left(r\right){[I-g^M\left({\lambda }^M(r)-{\lambda }^c\right)]}^{-\mathrm{one}}〉+\phi 〈{\lambda }^F\left(r\right){[I-g^F({\lambda }^f(r)-{\lambda }^c)]}^{-\mathrm{one}}〉\right]\times \\ {\left[(\mathrm{one}-\phi ){〈{[I-g^M({\lambda }^M(r)-{\lambda }^c)]}^{-\mathrm{one}}〉}^{-\mathrm{one}}+\phi 〈{[I-g^F({\lambda }^F(r)-{\lambda }^c)]}^{-\mathrm{one}}〉\right]}^{-\mathrm{one}}.\left(2\right)\end{array}$$

тензор теплопроводности флюида в точке r образца пористо-трещиноватого материала; I - единичная матрица. Компоненты тензора g имеют видIn formula (2), angle brackets mean volume averaging, which in the case of a statistically homogeneous medium can be replaced by statistical averaging over the ensemble. $${\lambda }^F(r)$$

fluid thermal conductivity tensor at point r of the sample of porous-fractured material; I is the identity matrix. The components of the tensor g have the form

$$g_{kl}=-\frac{\mathrm{one}}{\mathrm{four}\pi }{\displaystyle \int n_k{}_l{\Lambda }^{-\mathrm{one}}d\Omega ,\left(3\right)}$$

,

,

, dΩ≡sinθdθdφ, и a_i - полуоси эллипсоидов, моделирующих зерна минерального вещества (индекс M), поры и трещины (индекс F); $$\Lambda \equiv X_{ij}^c{n}_i{n}_j$$

, θ и φ - полярный и азимутальный угол в сферической системе координат. λ^c - тензор теплопроводности тела сравнения. Различный выбор тела сравнения приводит к различным формулам методов теории эффективных сред, включая метод самосогласования, предполагающем λ^c=λ^* (Popov et al. Interrelations between thermal conductivity and other physical properties of rocks: experimental data. Pure Appl. Geophys., 160, 2003, pp.1137-1161), метод Хашина-Штрикмана (Bayuk I., Gay J, Hooper J, and Chesnokov E. Upper and lower stiffness bounds for porous anisotropic rocks, Geophysics Journal International, 175, 2008, pp.1309-1320), в котором свойства тела сравнения полагают равными свойствам минерального вещества или флюида в зависимости от внутренней структуры породы. Выбор тела сравнения в виде λ^c=(1-f)λ^M+fλ^F, где f - некоторая константа, позволяет учесть степень связности порово-трещиноватого пространства (Bayuk I. and Chesnokov E. Identification of the fluid type in a reservoir rock, Journal of the Solid Earth, 35, Nr. 11, 1999, pp.917-923).where n _kl ≡n _k n _l ,

,

,

, dΩ≡sinθdθdφ, and a _i are the semiaxes of ellipsoids simulating mineral grains (index M), pores and cracks (index F); $$\Lambda \equiv X_{ij}^c{n}_i{n}_j$$

, θ and φ are the polar and azimuthal angles in the spherical coordinate system. λ ^c is the thermal conductivity tensor of the reference body. A different choice of the comparison body leads to different formulas of the methods of the theory of effective media, including the self-consistency method assuming λ ^c = λ ^* (Popov et al. Interrelations between thermal conductivity and other physical properties of rocks: experimental data. Pure Appl. Geophys., 160, 2003, pp. 1137-1161), Hashin-Shtrikman method (Bayuk I., Gay J, Hooper J, and Chesnokov E. Upper and lower stiffness bounds for porous anisotropic rocks, Geophysics Journal International, 175, 2008, pp. 1309- 1320), in which the properties of the comparison body are assumed to be equal to the properties of the mineral substance or fluid, depending on the internal structure of the rock. The choice of the comparison body in the form λ ^c = (1-f) λ ^M + fλ ^F , where f is a constant, allows us to take into account the degree of connectivity of the pore-fractured space (Bayuk I. and Chesnokov E. Identification of the fluid type in a reservoir rock Journal of the Solid Earth, 35, Nr. 11, 1999, pp. 917-923).

The determination of porosity, geometric parameters of the pore space and thermal conductivity of the matrix for a sample of a porous material from the results of measurements of the thermal conductivity of a fluid-saturated sample of a porous material can be achieved, for example, by minimizing the function characterizing the degree of deviation of the theoretical value of thermal conductivity from the experimental value of thermal conductivity obtained for a sample of porous material for each saturation. This function can be, for example, the sum of the squares of the deviations or the sum of the modules of the deviations of the theoretical and experimental values of thermal conductivity, while the summation is carried out according to the number of measurements of thermal conductivity of the sample of saturated porous material. Another example of finding a solution for porosity, geometric parameters of the pore space and thermal conductivity of a matrix for a sample of a porous material is the accumulation of all values of porosity, geometric parameters of pore space and thermal conductivity of the matrix, which provide a discrepancy between theoretical and experimental values of thermal conductivity obtained for a sample of a porous material at each saturation not exceeding a certain set value, and the subsequent calculation of statistical characteristics ISTIC for accumulated porosity values of geometrical parameters of pore space and the thermal conductivity of the porous material of the sample matrix.

In one embodiment, the thermal conductivity of a mixture of two or more fluids is determined by the known thermal conductivity of each of two or more mixed fluids and the proportion of volumes or masses of mixed fluids. Such a determination of the thermal conductivity of a mixture of N fluids can be carried out, for example, using the so-called theoretical average model. This model has the form (U.S. Patent No. 5159569. Formation evaluation n-om thermal properties. H. Xu and R. Desbrandes, 1992):

,

,

where λ of the _mixture is the thermal conductivity of the mixture of N fluids, N is the number of mixed fluids, S _{fluid i} is the relative volumetric content of the i-th fluid in the fluid mixture, λ _fluid i is the thermal conductivity of the i-fluid.

In order to make it less difficult to prepare mixtures of two or more fluids with a certain fixed thermal conductivity of the mixture, prepare mixtures of at least two fluids, and then after preparing each such mixture, the value of its thermal conductivity is determined experimentally. The thermal conductivity of the prepared mixture can be determined using any of the standard methods for measuring the thermal conductivity of fluids, for example, using the DTC-25 Thermal Conductivity Analyzer instrument manufactured by Intertech Corporation (USA).

An embodiment of the invention is possible when, in addition to each of the prepared mixtures of two or more fluids, the necessary thermal conductivity values or the thermal conductivity range of the prepared mixtures are predefined. The value of thermal conductivity or the thermal conductivity range of each mixture is set based on the necessary difference in thermal conductivity of one or more saturating fluids and different mixtures. The necessary difference in the thermal conductivities of the saturating fluid and mixtures is chosen so as to provide a stable solution to the problem of determining the porosity, geometric parameters of the pore space and thermal conductivity of the matrix for the sample of the porous material from the results of measurements of the thermal conductivity of the fluid-saturated sample of the porous material and the necessary accuracy in determining the porosity, geometric parameters of the pore space and thermal conductivity matrix samples of porous material.

The invention can be implemented in such a way that gas or different gases are used as at least one of the fluids in the preparation of the fluid mixture. Air can be used as gas.

In the latter case, the implementation of the invention is possible in such a way that variations in the thermal conductivity of the prepared mixture of source fluids and gas with known thermal conductivity and the required value of the thermal conductivity of this mixture are obtained by changing the humidity of the source gas, additionally saturating the gas with one or more fluids.

In accordance with one embodiment of the invention, in advance, taking into account the thermal conductivity of one or more saturating fluids, the necessary thermal conductivity values of two or more initial mixed fluids, the number of prepared initial fluid mixtures and the necessary thermal conductivity of prepared initial fluid mixtures are determined based on the stability of solving the inverse problem to determine the characteristics of the pore space and thermal conductivity of the matrix of the sample of porous material and accuracy Measurements of thermal conductivity fluids, mixtures of fluids and the porous material of the sample after each saturation. The necessary values of the thermal conductivity of the two source fluids, the number of prepared mixtures of the source fluids and the necessary values of the thermal conductivity of the prepared mixtures of the source fluids can be determined, for example, by requiring the simultaneous fulfillment of the following three conditions. The first condition is that the thermal conductivity of the mixtures of the selected fluids should differ by an amount exceeding the accuracy of measuring thermal conductivity in the method used to measure the thermal conductivity of the mixtures of two selected fluids. For example, when using the linear source method, which provides measurements of the thermal conductivity of fluids with an error of 10%, the thermal conductivity of mixtures of selected fluids should differ by more than 10%. The second condition is that the values of the thermal conductivity of the sample of the porous material at each saturation calculated by the theoretical method used to determine the characteristics of the pore space and thermal conductivity of the matrix of the sample of the porous material must differ by an amount exceeding the accuracy of measuring thermal conductivity in the method used to measure thermal conductivity sample of saturated porous material. For example, the theoretical values of thermal conductivity calculated for a sample of a porous material saturated with various mixtures of two selected fluids should differ by more than 3% if the optical scanning method is used to measure the thermal conductivity of a sample of porous material (the accuracy of measurements by optical scanning is 2-3%) . The third condition is that two or more fluids used to prepare the saturating mixtures are selected so that their thermal conductivity ensures that at least one mixture of two or more fluids satisfies the first and second conditions.

In accordance with another embodiment of the invention, the porosity of the porous material sample is further determined. The porosity is determined before or after the thermal conductivity measurements of a sample of a porous material, sequentially saturated with one or more fluids and at least one selected mixture of fluids with known thermal conductivity. The measured values of thermal conductivity for a sample of a porous material at each saturation and the known value of porosity of a sample of porous material are used to determine the geometric characteristics of the pore space and thermal conductivity of the matrix of a sample of porous material, using well-known relationships that relate the measured value of thermal conductivity to known values of porosity, thermal conductivity of fluids and one or more fluid mixtures with the desired geometric characteristics of the pore space conductivity sample matrix.

The method may further include measuring one or more additional physical properties of the porous material sample after each saturation of the porous material sample with a fluid or a mixture of fluids with known thermal conductivity. Such physical properties can be, for example, elastic wave velocities, electrical conductivity, dielectric or hydraulic permeability, density, bulk heat capacity. After that, the results of determining one or more additional physical properties of the sample of the porous material are used together with the results of determining the thermal conductivity to determine the characteristics of the pore space and thermal conductivity of the matrix of the sample of the porous material. For this purpose, in addition to relations (1) - (3), relating the measured thermal conductivity and the geometric parameters of the pore space, the porosity and thermal conductivity of the matrix, similar relations of the theory of effective media are used, which allow us to connect the measured physical property with the geometric parameters of the pore space, porosity and the corresponding physical properties matrices. Moreover, the formulas for any effective transport property (electrical conductivity, dielectric and hydraulic permeability) have the form similar to formulas (1) - (3) for effective thermal conductivity with the replacement of the thermal conductivity tensor by the electrical conductivity tensor, dielectric or hydraulic permeability.

If the velocities of elastic waves are measured, then the formulas connecting the measured velocities of elastic waves with the characteristics of the pore space and the thermal conductivity of the matrix have the following form. If the velocity measurements of elastic waves are carried out in a direction specified in the main coordinate system by the vector n = (n ₁ , n ₂ , n ₃ ), then in this direction the values of the velocities of elastic waves are determined through the density and effective tensor of elasticity according to the well-known Green-Christoffel equation :

$$\det (G_{ik}-e{({\upsilon }^{(n)})}^2{\delta }_{ik})=0\left(\mathrm{four}\right)$$

Where

$$G_{ik}=C_{ijkl}^{*}{n}_j{n}_l.\left(5\right)$$

- компоненты эффективного тензора упругости. Эффективный тензор упругости определяется по формуле, аналогичной формуле (2), с заменой тензоров теплопроводности на тензоры упругости, единичного тензора второго ранга на единичный тензор четвертого ранга, тензора g второго ранга на тензор g четвертого ранга, который имеет видIn formulas (4) and (5), ν ⁽ⁿ⁾ is the velocity of a longitudinal or transverse wave in the n direction, ρ is the density, δ _ik is the Kronecker symbol, $$C_{ijkl}^{*}$$

- components of the effective tensor of elasticity. The effective elasticity tensor is determined by a formula similar to formula (2), with the replacement of the thermal conductivity tensors by the elastic tensors, the unit tensor of the second rank by the unit tensor of the fourth rank, the tensor g of the second rank by the tensor g of the fourth rank, which has the form

,

,

, n_mn≡n_mn_n,

,

,

. $${\Lambda }_{kl}\equiv C_{km\ln }^{*}{n}_{mn}$$

, n _mn ≡n _m n _n ,

,

,

.

If volumetric heat capacity or porosity is measured along a sample of pore-fractured material, then the relations between their measured values and the corresponding values of the matrix, saturating fluid and porosity are

$${(c\rho )}^{(n)}={(c\rho )}^{*}=(\mathrm{one}-\phi ){(c\rho )}^M+\phi {(c\rho )}^F,(7)$$

$${\rho }^{(n)}=\rho *=(\mathrm{one}-\phi ){\rho }^M+\phi {\rho }^F.\left(8\right)$$

Volumetric heat capacity and porosity are independent of the geometric parameters of the pore space.

The determination of porosity, geometrical parameters of the pore space and the thermal conductivity of the matrix for a sample of a porous material can be achieved, for example, by minimizing the function characterizing the degree of deviation of the theoretical value of thermal conductivity and other measured physical properties from the experimental value of thermal conductivity and other measured physical quantities obtained for the sample at each saturation. This function can be, for example, the sum of the squares of the relative deviations or the sum of the modules of the relative deviations of the theoretical and experimental values of thermal conductivity and other physical quantities. Moreover, the summation is carried out according to the number of measurements of physical properties. Another example of finding a solution for the porosity, geometric parameters of the pore space and thermal conductivity of the matrix for a sample of a porous material is the accumulation of all values of porosity, geometric parameters of the pore space and thermal conductivity of the matrix, which provide a discrepancy between the theoretical and experimental values of thermal conductivity and other physical quantities obtained for the sample for each its saturation, not exceeding a certain set value, and the subsequent calculation of statistical Characteristics for the accumulated values of the porosity, the pore space of geometrical parameters and the thermal conductivity of the matrix.

. Для вытянутых эллипсоидов с аспектным отношением κ, большим 1, имеет место соотношение $$D_3=\left(1-e^2\right)\frac{Arth(e)-e}{e^3}$$

, $$e=\sqrt{\frac{{к}^2-1}{{к}^2}}$$

, а для сплюснутых эллипсоидов с аспектным отношением κ, меньшим или равным 1, $$D_3=\left(1+e^2\right)\frac{e-arctg(e)}{e^3}$$

, $$e={\left[\frac{1-{к}^2}{{к}^2}\right]}^{1/2}$$

. Распределение объема трещин и пор по фактору деполяризации описывается двупараметрическим Бэта-распределением $$Р(F)=\frac{Г(\alpha +\beta )}{Г(\alpha )Г\left(\beta \right)}{F}^{\alpha -1}{(1-F)}^{\beta -1}$$

, где _I - гамма-функция. Параметры Бета-распределения и неотрицательны и считаются неизвестными. Поскольку порода изотропная, то ориентация трещин и пор считается хаотической.As an example of the implementation of the invention, in accordance with this, we consider the case when determining the characteristics of the pore space and thermal conductivity of the matrix should be performed on a sample of a carbonate reservoir with a diameter of 5 cm and a length of 5 cm. Water and oil were chosen as saturating fluids, whose thermal conductivity is 0.6 and 0.12 W / ( mK). Five mixtures of these fluids were prepared in the water / oil ratio, with values of 0.9 / 0.1 (mixture 1), 0.6 / 0.4 (mixture 2), 0.4 / 0.6 (mixture 3), 0.2 / 0.8 (mixture 4) and 0.0 / 1.0 (mixture 5). The thermal conductivity of the mixtures of two fluids is measured by the linear source method and according to the measurement results is 0.50, 0.30, 0.22, 0.15 and 0.12 W / (m · K) for mixtures 1-5, respectively. The difference in thermal conductivity of the mixtures is more than 15%, which exceeds the accuracy of the linear source method (10%). The sample is sequentially saturated under vacuum of each of these mixtures. The vacuum unit is used to completely saturate related cracks and pores with water. After each saturation, the thermal conductivity of the fluid-saturated sample is measured by optical scanning. After each measurement of thermal conductivity, the sample is extracted (to remove oil) and dried to 105 ° C. Then the following mixture is saturated. The measured thermal conductivity of a sample saturated with mixtures 1–5 is 2.19, 2.04, 1.93, 1.83, and 1.77 W / (m · K), respectively. The difference in thermal conductivity of a sample saturated with various mixtures exceeds the accuracy of the linear source method (2-3%). The obtained values of thermal conductivity are used to determine the geometric parameters of the pore space, porosity and thermal conductivity of the matrix. The shape of the cracks and pores, on which the g value in equation (3) depends, is modeled by rotation ellipsoids, which are characterized by an aspect ratio. In this case, it is convenient to use the depolarization factor D, which is associated with the aspect ratio according to the formula $$D=\frac{\mathrm{one}-{\mathrm{<figure-callout\; id="3"\; label="D"\; filenames="00000029.png"\; state="\{\{state\}\}">D</figure-callout>}}_3}{2}$$

. For elongated ellipsoids with an aspect ratio κ greater than 1, the relation $$D_{}$$$${}_3=\left(\mathrm{one}-e^2\right)\frac{Arth(e)-\mathrm{<figure-callout\; id="3"\; label="e\; e"\; filenames="00000029.png"\; state="\{\{state\}\}">e\; </figure-callout>}}{e^{}}$$

, $$e=\sqrt{\frac{{\mathrm{to}}^2-\mathrm{one}}{{\mathrm{to}}^2}}$$

, and for flattened ellipsoids with an aspect ratio κ less than or equal to 1, $${\mathrm{<figure-callout\; id="3"\; label="D"\; filenames="00000029.png"\; state="\{\{state\}\}">D</figure-callout>}}_3=\left(\mathrm{one}+e^2\right)\frac{e-arctg(e)}{{\mathrm{<figure-callout\; id="3"\; label="e"\; filenames="00000029.png"\; state="\{\{state\}\}">e</figure-callout>}}^3}$$

, $$e={\left[\frac{\mathrm{one}-{\mathrm{to}}^2}{{\mathrm{to}}^2}\right]}^{\mathrm{one}/2}$$

. The distribution of the volume of cracks and pores by the depolarization factor is described by a two-parameter Beta distribution $$R(F)=\frac{G(\alpha +\beta )}{G(\alpha )G\left(\beta \right)}{F}^{\alpha -\mathrm{one}}{(\mathrm{one}-F)}^{\beta -\mathrm{one}}$$

where _I is the gamma function. Beta distribution parameters are both non-negative and considered unknown. Since the rock is isotropic, the orientation of cracks and pores is considered chaotic.

The unknown quantities included in formula (2) are two Beta distribution parameters, matrix thermal conductivity, and open porosity. To find a solution, the areas of possible changes of each of the unknown quantities are set. For each of the Beta distribution parameters, this range of change is the interval [0.0001; one hundred]. For this sample, the range of variation in porosity is selected equal to 15-25%, based on the log data on porosity for the interval of depths from which the sample was extracted. Matrix thermal conductivity is different from thermal conductivity determined by the mineral composition, since the carbonate reservoir may contain isolated pores, as well as residues of organic matter and capillary water. The change in the matrix thermal conductivity is set in the range of its possible values of 2.5-3.5 W / (m · K). The unknown Beta distribution parameters, matrix thermal conductivity, and open porosity are determined by minimizing the sum of the relative residuals of the theoretical and experimental thermal conductivities obtained for each saturating fluid. To minimize, a version of the deformable polyhedron method is used, which allows one to take into account the range of possible changes in the desired parameters. Figure 1 shows the distribution of the volume of voids in aspect ratio, built on the found values of the Beta distribution parameters. The found value of the matrix thermal conductivity is 2.96 W / (m · K), and the open porosity is 20%. The found value of open porosity coincides with the value of porosity, which was then measured for this sample by the Archimedes method for testing the proposed method.

The thermal conductivity of a fluid mixture (e.g., water and oil) can be calculated using the well-known Lichtenecker method (Lichtenecker, K. and K. Rother, Die Herleitung des logarithmischen Mischungsgesetzes aus allgemeinen Prinzipien des stationaren StrOmung, Phys. Zeit, 1931, 32, 255 -260).

The fluid mixture can be made in such a way that the thermal conductivity of the mixtures does not exceed twice the thermal conductivity calculated by the known values of thermal conductivity and volume concentration of the components composing the matrix. To calculate this value of thermal conductivity, the well-known Lichtenekker method is used.

When using air as one of the initial fluids, several mixtures can be made by changing the air humidity so that the thermal conductivity of the mixtures differs by no less than 10%.

Preliminarily, the value of the thermal conductivity of the matrix can be estimated from the known values of the thermal conductivity and volume concentration of the components composing the matrix. For this, the well-known Lichteneker method is used. Then, the initial saturating fluids are selected so that the thermal conductivity of one of the fluids differs from the estimated value of the thermal conductivity of the matrix by at least an order of magnitude, and the thermal conductivity of the second fluid is not less than five times. The porosity of the sample is not less than 10%. In this case, the thermal conductivity of the fluids differs by more than two times. One or more mixtures of these two fluids are made in such a way that the thermal conductivity of each mixture differs by no less than 15% from the thermal conductivity of any other mixture and pure fluids. This value exceeds the accuracy of measuring the thermal conductivity of fluids by the linear source method (10%). Moreover, the thermal conductivity of each mixture differs no less than two times from the estimated value of the thermal conductivity of the matrix. Such a contrast of the properties of saturating fluids and their mixtures provides a difference in the thermal conductivity of a sample of a porous material saturated with each fluid and their mixture or mixtures, obviously exceeding the accuracy of thermal conductivity measurements by optical scanning (2-3%), which is used to measure the thermal conductivity of a saturated sample of a porous material. A significant difference in the thermal conductivity of a sample of a porous material saturated with each fluid and their mixture or mixtures leads to a stable solution of the inverse problem of determining the characteristics of the pore space and thermal conductivity of the matrix of a sample of a porous material.

As another example implementation of the invention, consider the case where porosity is known for a carbonate reservoir sample. Thermal conductivity measurements are carried out for the same sample and with the same saturating mixtures of two fluids (water and oil), as in the previous description of the implementation example. The thermal conductivity of fluid mixtures, as in the previous description of the example implementation, is measured by the linear source method. The porosity, measured by the method of Archimedes, is 20%. The unknown quantities in formula (2) are two Beta distribution parameters and matrix thermal conductivity, which are found by minimizing the sum of the relative discrepancies of the theoretical and experimental thermal conductivities obtained for each saturating fluid. The found value of the matrix thermal conductivity is 2.98 W / (m · K). The distribution of the void volume by aspect ratios, constructed from the found values of the Beta distribution parameters, is shown in Fig. 1b.

In addition to thermal conductivity, for example, the longitudinal and transverse velocities of elastic waves and the electrical conductivity of a sample can be measured. The measured values are used together to determine the characteristics of the pore space and thermal conductivity of the matrix.

Claims (14)

1. A method for determining the characteristics of the pore space and thermal conductivity of a matrix of samples of porous materials, according to which the porous material sample is alternately saturated with at least two fluids with different known thermal conductivities, wherein at least one saturating fluid uses a mixture of fluids of at least two fluids with different known thermal conductivity, after each saturation of the sample, the thermal conductivity of the saturated sample of the porous material is measured, the characteristics and pore space and the thermal conductivity of the porous matrix material sample taking into account the thermal conductivity measurements. 2. The method of determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, according to which the characteristics of the pore space include porosity and geometric parameters of the pore space. 3. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, in accordance with which the porosity of the samples of porous materials is preliminarily determined. 4. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, in accordance with which the thermal conductivity of the fluid mixture is preliminarily determined from the known thermal conductivity of each of the mixed fluids and the proportion of volumes or masses of the mixed fluids. 5. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, in accordance with which the thermal conductivity of the fluid mixture is preliminarily determined by measuring the thermal conductivity of the mixture after mixing the fluids. 6. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, according to which for the fluid mixture, the thermal conductivity value or the thermal conductivity range of the prepared mixture is pre-set. 7. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of porous materials according to claim 1, according to which oil and water are used as fluids. 8. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, according to which, at least one of the fluids of the mixture uses a gas with known thermal conductivity. 9. The method of determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 8, according to which, when using at least two fluid mixtures containing gas with known thermal conductivity, different thermal conductivity of the mixtures is achieved by using the same gas with different humidity. 10. A method for determining the characteristics of pore space and thermal conductivity of a matrix of samples of porous materials according to claim 8 or 9, according to which air is used as a gas with known thermal conductivity. 11. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, according to which the necessary values of the thermal conductivity of the fluids, the number of prepared fluid mixtures and the thermal conductivity of the prepared fluid mixtures are preliminarily determined. 12. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, according to which after each saturation of the sample of porous material, at least one additional physical property of the sample is measured, and the results of determining the additional physical property of the sample of porous material are used together with the results of determining the thermal conductivity of a sample of a porous material to determine the characteristics of the pore space and thermal conductivity of the matrix sample of porous materials. 13. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to item 12, according to which the additionally determined physical property of the sample of porous material is at least one property from the following group: elastic wave velocity, electrical conductivity, permeability, density, bulk heat capacity. 14. The method for determining the characteristics of the pore space and thermal conductivity of the matrix of samples of porous materials according to claim 1, according to which the thermal conductivity of a saturated sample is determined by optical scanning.

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